CN101345618A - Encryption and decryption method for four-item weight FRFT communication based on variable parameter - Google Patents

Abstract

The invention relates to encryption and decryption method for tetrachoric weighting FRFT communication, belonging to communication field. In the existing technology, non target receiver can decipher enciphered signal by scanning one by one of enciphered parameter when known transmitter enciphered signal by tetrachoric weighting FRFT. To solve the above-mentioned problem, the inventive method comprises that data source is modulated at transmitter by base band to deliver to encipher module which executes tetrachoric weighting FRFT controlled under alpha, MV and NV determined by pseudorandom code and matched parameter change pattern, enciphered signal modulated by digital carrier is delivered to channel for transmitting via D/A conversion and up converter; data collected by down converter and A/D is delivered to decription module for digital carrier coherent demodulation, deciphered signal is obtained after tetrachoric weighting FRFT controlled by alpha, MV and NV determined by parameter change pattern, and pseudorandom code, then base band demodulation is operated.

Description

Based on maintaining secrecy and decryption method of the four-item weight FRFT of variable element communication

Technical field

The present invention relates to communication technical field, be specifically related to the signal processing and maintaining secrecy and decryption method of communicating by letter of FRFT (fractional Fourier transform).

Background technology

FRFT is a kind of important time frequency analyzing tool, has obtained comparatively extensive studies in the last few years, and is used in some field of engineering technology.FRFT is the popularization to traditional Fourier transform, and its essential characteristics can be understood as the fractionation to the Fourier transform characteristic value.The continuity of parameter value, rotation additivity and be the fundamental property of FRFT to the uniformity of signal time-frequency form.FRFT roughly is divided into: classical class FRFT and weighting class FRFT.

Classical class FRFT is a kind of FRFT form that proposes relatively early, and it is promoted with complete directly from Fourier transform integral kernel and characteristic value.Because the orthogonal basis of classical FRFT with chirp (Qie Pu) form, thereby the classical class FRFT chirp class FRFT that is otherwise known as.Research and application about FRFT at present concentrates on the classical class mostly, and classical FRFT has application more widely in finding the solution scientific researches such as the differential equation, quantum mechanics, signal analysis and processing; The engineering aspect is to utilize classical FRFT the earliest as optical correlation fields such as optical communication system, light image processing, also is that application is the most successful at present.But be subject to the discrete logarithm problem of classical FRFT, its application in the communications field has been subjected to bigger restriction.

Weighting class FRFT (WFRFT) is a kind of new mathematical tool that is different from classical class FRFT, its mathematical property has obtained good embodiment in optical system, and can be realized by simple optics, thereby in Information Optics, be used widely.

Along with going deep into that FRFT is studied, the definition of WFRFT is constantly promoted, and unified with classical class FRFT to a certain extent.WFRFT definition form goes for any periodic conversion that has.Utilize this character, continuous WFRFT definition can be generalized to the WFRFT of discrete series.

The continuous four-item weight score Fourier conversion (4-WFRFT) of tradition is defined as:

F ^α[f(t)]＝a ₀(α)f(t)+a ₁(α)F(t)+a ₂(α)f(-t)+a ₃(α)F(-t)

A wherein ₀～a ₃Be the weight coefficient by the control of dynamic encryption parameter alpha, the form of embodying is:

$a_l\left(\mathrm{\α}\right)=\cos \left(\frac{(\mathrm{\α}-l)\mathrm{\π}}{4}\right)\cos \left(\frac{2(\mathrm{\α}-l)\mathrm{\π}}{4}\right)\exp (\±\frac{3(\mathrm{\α}-l)\mathrm{\πi}}{4}),(l=\mathrm{0,1,2,3})$

The value cycle of dynamic encryption parameter alpha is 4, and the span of setting α here is any real number between [0,4] or [2,2], for the real number outside the span, and weight coefficient a _l(l=0,1,2,3) will present cyclic variation along with α.The result of 4-WFRFT is f (t) when α=0, and the result of 4-WFRFT is F (t) when α=1.Wherein f (t) is the function that is transformed, and f (is the counter-rotating function at center with the initial point for f (t) t); F (t) becomes the right function of Fourier transform with f (t), and F (is the counter-rotating function at center with the initial point for F (t) t).

The 4-WFRFT of the discrete series of being promoted by the continuous 4-WFRFT of tradition is defined as:

F ^α[x(n)]＝w ₀(α)x(n)+w ₁(α)X(k)+w ₂(α)x(-n)+w ₃(α)X(-k)

Wherein

$w_l\left(\mathrm{\α}\right)=\frac{1}{4}\underset{i=0}{\overset{3}{\mathrm{\Σ}}}\exp \{\±\frac{2\mathrm{\πi}}{4}[({4m}_i+1)\mathrm{\α}(k+{4n}_i)-\mathrm{lk}\left]\right\},(l=\mathrm{0,1,2,3})$

Be by α, MV=[m ₀, m ₁, m ₂, m ₃] and NV=[n ₀, n ₁, n ₂, n ₃] the common weight coefficient form of controlling of these 9 parameters, wherein MV and NV are real vector.When MV and NV are 0, w _lWith a _lDefinition coefficient equivalence.X (n) and X (k) are that discrete Fourier transform (DFT) (DFT) is right, and DFT adopts following formal definition:

$\left\{\begin{array}{c}X\left(k\right)=\frac{1}{\sqrt{N}}\underset{n=0}{\overset{N-1}{\mathrm{\&Sigma;}}}x\left(n\right)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="A20081013694100111.png,A20081013694100121.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{N}\mathrm{kn}}\\ x\left(n\right)=\frac{1}{\sqrt{N}}\underset{k=0}{\overset{N-1}{\mathrm{\&Sigma;}}}X\left(k\right){\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="A20081013694100111.png,A20081013694100121.png"\; state="\{\{state\}\}">e</figure-callout>}}^j\end{array}\right.$

The 4-WFRFT of the discrete series of promoting has inherited all character of traditional continuous 4-WFRFT, can come the rotation of the periodicity and the characteristic vector of control change in addition by the adjustment to real vector M V and NV.In a word, the 4-WFRFT of the discrete series of popularization is complicated more, but more complete in theory, and is more flexible and changeable during practical application.

Application number is 200810063871.2, exercise question is the patent application of " a kind of communication security and decryption method based on four-item weight score Fourier conversion ", when non-purpose receiver known transmitter employing is that four-item weight score Fourier conversion carries out signal encryption, when particularly encryption parameter is comparatively simple, non-purpose receiver just can crack coded signal by encryption parameter is scanned one by one, thereby obtains actual signal.

Summary of the invention

The objective of the invention is for solving what adopt when non-purpose receiver known transmitter is that four-item weight score Fourier conversion carries out signal encryption, when particularly encryption parameter is comparatively simple, adopt a kind of communication security and non-purpose receiver of decryption method just can crack coded signal by encryption parameter is scanned one by one based on four-item weight score Fourier conversion, thereby obtain the problem of actual signal, the existing secret and decryption method that proposes based on the four-item weight FRFT communication of variable element.

The secret of four-item weight FRFT communication based on variable element of the present invention realized by following steps with decryption method: at transmitter terminal, data source is given encrypting module through after the baseband modulation, encrypting module carries out four-item weight score Fourier conversion to data under the control of dynamic encryption parameter alpha, the real vector M V of dynamic encryption and NV, transmit through sending into channel after the upconverter through the D/A conversion through the coded signal behind the digital carrier modulation module again; At receiver end, be sent to deciphering module through the data after low-converter and the A/D sampling, in deciphering module, at first pass through digital carrier coherent demodulation module, then after the four-item weight score Fourier conversion that the dynamic deciphering parameter-α of process, the closely knit vector M V of dynamic resolution, NV control again, obtain decrypted signal, carry out base band demodulating work then; Real vector M V of described dynamic encryption parameter alpha, dynamic encryption and NV, dynamically deciphering parameter-α and the closely knit vector M V of dynamic resolution and NV all uses the dynamic parameter selection module of same structure to realize encrypting or deciphering parameter dynamically changes work, this change all is to produce by the pseudo noise code of special speed with parameter changing pattern that pseudo noise code adapts.

In the present invention, on the selection principle of dynamic encryption parameter alpha any real number, but because periodic the existence, α chooses the real number between [0,4] or [2,2] usually.For fixing α, have only the criterion of an optimum to recover original information signal in theory from the signal after encrypting, promptly the signal after encrypting is done the four-item weight class fractional Fourier transform of parameter for-α.Because the flexibility that α selects makes system user to encrypt signal according to the different encryption parameter of actual conditions Dynamic Selection.When selection of parameter is proper, coded signal will present class Gauss's distribution character.

In order to resist of the scanning of non-purpose receiver, introduce real vector M V of dynamic encryption and NV to encryption parameter α.When dynamic encryption reality vector M V=NV=0, when if input signal is the random signal of process digital modulation (MPSK or MQAM), change along with parameter alpha, the real part of signal and imaginary part will be distinguished Gaussian distributed after the conversion, these characteristics make the signal after the conversion have and the white Gaussian noise similarity, and then can play the effect of signal encryption; When the real vector M V of dynamic encryption and NV are not zero entirely; signal after the conversion will present more complicated variation; can be so that the variation of " constellation division " appears in the signal after the conversion; and then with the camouflage after modulation constellation protect original modulation intelligence; just the number of constellation points of Ju Jiing is counted many than modulation constellation before encrypting; utilize this characteristic can confuse non-purpose receiver, make it do the judgement that makes mistake.

Advantage of the present invention is: directly the 4-WFRFT with discrete series is incorporated in the communication system, can under the condition of occupying volume external spectrum resource not, encrypt data-signal, the complexity and the fast fourier transformation algorithm of its realization are suitable, and it is less to take system hardware resources, are easy to realize.The core cell of encrypt and decrypt is identical, it all is the four-item weight score Fourier conversion module, so multiplexing when being easy to duplex communication, owing to adopted the variation of pseudo random sequence control encrypt and decrypt parameter, make that the variation of encrypting the back signal is complicated more, be difficult to be cracked by direct parameter scanning.

Description of drawings

Fig. 1 is based on the structural representation of the secure communication device of variable element four-item weight class fractional Fourier transform; Fig. 2 is the schematic diagram of the dynamic change strategy of dynamic encryption parameter alpha, transverse axis express time wherein, and the longitudinal axis is represented encryption parameter; Fig. 3 is that each isolated component in real vector M V of dynamic encryption and NV adopts same PN sequence, and the PN sequence is in the period T of parameter saltus step _CIn 4 frame period T are arranged _FThe time, the schematic diagram of the variation strategy of real vector M V of dynamic encryption and NV; Fig. 4 is that each isolated component in real vector M V of dynamic encryption and NV adopts same PN sequence, and the PN sequence is in the period T of parameter saltus step _CIn 16 frame period T are arranged _FThe time, the schematic diagram of the variation strategy of real vector M V of dynamic encryption and NV; Fig. 5 is the schematic diagram of the variation strategy when the real vector M V of dynamic encryption adopts different PN sequences with each isolated component among the NV or adopt the different original position of same PN sign indicating number.

Embodiment

Embodiment one: present embodiment is described below in conjunction with Fig. 1.Present embodiment realizes by following step with decryption method by described the secret of four-item weight FRFT communication based on variable element: at transmitter terminal, data source is given encrypting module through after the baseband modulation, encrypting module carries out four-item weight score Fourier conversion to data under the control of dynamic encryption parameter alpha, the real vector M V of dynamic encryption and NV, transmit through sending into channel after the upconverter through the D/A conversion through the coded signal behind the digital carrier modulation module again; At receiver end, be sent to deciphering module through the data after low-converter and the A/D sampling, in deciphering module, at first pass through digital carrier coherent demodulation module, then after the four-item weight score Fourier conversion that the dynamic deciphering parameter-α of process, the closely knit vector M V of dynamic resolution, NV control again, obtain decrypted signal, carry out base band demodulating work then; Described dynamic encryption parameter alpha, the real vector M V of dynamic encryption and NV, dynamic deciphering parameter-α, the closely knit vector M V of dynamic resolution and NV all can use the dynamic parameter selection module of same structure to realize that encryption or deciphering parameter dynamically change work, they all are the pseudo noise codes by the special speed of clock source control pseudo-code generator output, and be stored in the command decoder the common decision of parameter changing pattern that the pseudo noise code with described special speed adapts, according to actual conditions, they can adopt identical clock source and the identical multiplexing mode of pseudo-code generator.

In the present embodiment, on the selection principle of dynamic encryption parameter alpha any real number, but because periodic the existence, α chooses the real number between [0,4] or [2,2] usually.For fixing α, have only the criterion of an optimum to recover original information signal in theory from the signal after encrypting, promptly the signal after encrypting is done the four-item weight class fractional Fourier transform of parameter for-α.Because the flexibility that α selects makes system user to encrypt signal according to the different encryption parameter of actual conditions Dynamic Selection.When selection of parameter is proper, coded signal will present class Gauss's distribution character.

In order to resist of the scanning of non-purpose receiver, introduce real vector M V of dynamic encryption and NV to encryption parameter α.When dynamic encryption reality vector M V=NV=0, when if input signal is the random signal of process digital modulation (MPSK or MQAM), change along with parameter alpha, the real part of signal and imaginary part will be distinguished Gaussian distributed after the conversion, these characteristics make the signal after the conversion have and the white Gaussian noise similarity, and then can play the effect of signal encryption; When the real vector M V of dynamic encryption and NV are not zero entirely; signal after the conversion will present more complicated variation; can be so that the variation of " constellation division " appears in the signal after the conversion; and then with the camouflage after modulation constellation protect original modulation intelligence; just the number of constellation points of Ju Jiing is counted many than modulation constellation before encrypting; utilize this characteristic can confuse non-purpose receiver, make it do the judgement that makes mistake.

The concrete steps of encrypting are:

One, the signal to be encrypted that becomes plural form after the binary data process baseband modulation that data source provides gives encrypting module to encrypt, and wherein the baseband modulation mode is MPSK or MQAM digital modulation mode;

Two, encrypting module is encrypted four data sequences respectively simultaneously frame by frame, and the frame length of data sequence is the length of discrete Fourier transform (DFT), can select flexibly according to actual conditions, chooses 2 integral number power usually.The core of encrypting promptly is weighted summation to the data sequence, and four data sequences are followed successively by: sequence after the sequence after the be-encrypted data sequence of input, the be-encrypted data sequence process discrete Fourier transform (DFT), the be-encrypted data sequence process counter-rotating resume module and be-encrypted data sequence are successively through the sequence after discrete Fourier transform (DFT) and the counter-rotating resume module; According to encryption parameter α and the real vector M V of dynamic encryption, the NV of Dynamic Selection, and by coefficient generation module generation weight coefficient w ₀, w ₁, w ₂, w ₃Be weighted summation to being weighted data sequence;

Three, the sequence of complex numbers after the weighting is carried out digital carrier modulation back output, be the signal after the encryption.

The concrete steps of deciphering are:

(1), after the data that receive is changed through A/D, the coherent demodulation of at first carrying out digital carrier obtains in-phase component and quadrature component, and carrying out the Synchronous Processing of sequence after as the corresponding addition of imaginary part as real part, quadrature component with in-phase component, output sequence is sequence of complex numbers to be deciphered synchronously;

(2), to do parameter be the four-item weight class fractional Fourier transform of MV and NV for-α, the closely knit vector of dynamic resolution to the sequence of complex numbers for the treatment of deciphering, detailed process is identical with ciphering process, sequence after the conversion is the sequence after the deciphering, can transfer to the base band demodulating module and carry out next step work.

The dynamic change strategy of dynamic encryption parameter alpha is described: the complete period B of dynamic encryption parameter alpha in conjunction with Fig. 3 _α=4 have been divided into 8 groups, promptly are divided into α ₁, α ₂, α ₃, α ₄, α ₅, α ₆, α ₇And α ₈, each group is divided into 2 parts again, and wherein same group two parts at a distance of 2, correspond respectively to pseudo noise code and be 0 and the interval of 1 o'clock output parameter.B _FBe the size between each group parameter region, the parameter protection scope when also being each frame data conversion.T _FBe the time that each frame data continues, T _CBe the cycle of parameter saltus step, T in the strategy shown in the figure _C=3T _F, this ratio can be adjusted as required.The order of parameter transformation is in the strategy: α ₁, α ₆, α ₇, α ₃, α ₈, α ₂, α ₄, α ₅..., this is to set in advance in proper order, also can adjust as required in good time.

Illustrate that in conjunction with Fig. 3, Fig. 4 and Fig. 5 the variation strategy of real vector M V of dynamic encryption and NV is:

A, the variation strategy when each isolated component among real vector M V of dynamic encryption and the NV adopts same PN (pseudo noise code) sequence are:

A, in conjunction with Fig. 3 explanation when the period T of PN sequence in the parameter saltus step _CIn 4 frame period T are arranged _FThe time, the one-component m in the corresponding successively real vector of the frame of each PN sequence _iOr n _i(l=0,1,2,3), each component have only two kinds of value condition, and promptly 0 or 1.

B, in conjunction with Fig. 4 explanation when the period T of PN sequence in the parameter saltus step _CIn 16 frame period T are arranged _FThe time, the one-component in the corresponding real vector of per 4 PN sequence chips, promptly each component equals the decimal number that one 4 bit is represented.

C, when the period T of PN sequence in the parameter saltus step _C4 frame period T of interior less than _FThe time, with the period T of PN sequence in the parameter saltus step _CIn carry out periodic extension and make it have 4 frame period T _FAfter, implementation strategy a again.

D, when the period T of PN sequence in the parameter saltus step _C16 frame period T of interior less than _FThe time, with the period T of PN sequence in the parameter saltus step _CIn carry out periodic extension and make it have 4 frame period T _FAfter, implementation strategy b again.

B, in conjunction with Fig. 5 explanation variation strategy when the real vector M V of dynamic encryption adopts different PN sequences with each isolated component among the NV or adopt the different original position of same PN sign indicating number be: each isolated component is according to the rule variation of the PN sequence that is adopted.

Present embodiment all can be realized by DSP (Digital Signal Processing), FPGA (field programmable gate array) or FPGA+DSP.Present embodiment can adopt the system configuration of parallel or serial, and wherein parallel organization is more suitable in FPGA, and serial structure is more suitable in DSP; If adopt FPGA+DSP or other hardware structures, then can be according to the suitable Adjustment System structure of actual conditions.

Claims (6)

1, maintaining secrecy and decryption method based on the four-item weight FRFT of variable element communication, at transmitter terminal, data source is given encrypting module through after the baseband modulation, encrypting module carries out four-item weight score Fourier conversion to data under the control of dynamic encryption parameter alpha, the real vector M V of dynamic encryption and NV, transmit through sending into channel after the upconverter through the D/A conversion through the coded signal behind the digital carrier modulation module again; At receiver end, be sent to deciphering module through the data after low-converter and the A/D sampling, in deciphering module, at first pass through digital carrier coherent demodulation module, then pass through dynamic deciphering parameter-α again, the closely knit vector M V of dynamic resolution, after the four-item weight score Fourier conversion of NV control, obtain decrypted signal, carry out base band demodulating work then, it is characterized in that described dynamic encryption parameter alpha, real vector M V of dynamic encryption and NV, dynamically deciphering parameter-α and the closely knit vector M V of dynamic resolution and NV all use the dynamic parameter selection module of same structure to realize encrypting or deciphering parameter dynamically changes work, and this change all is to produce by the pseudo noise code of special speed with parameter changing pattern that pseudo noise code adapts.

What 2, the four-item weight FRFT based on variable element according to claim 1 communicated by letter maintains secrecy and decryption method, it is characterized in that the concrete steps of encrypting are:

One, the signal to be encrypted that becomes plural form after the binary data process baseband modulation that data source provides gives encrypting module to encrypt, and wherein the baseband modulation mode is MPSK or MQAM digital modulation mode;

Two, encrypting module is encrypted four data sequences respectively simultaneously frame by frame, and the frame length of data sequence is the length of discrete Fourier transform (DFT), chooses 2 integral number power; The core of encrypting promptly is weighted summation to the data sequence, and four data sequences are followed successively by: sequence after the sequence after the be-encrypted data sequence of input, the be-encrypted data sequence process discrete Fourier transform (DFT), the be-encrypted data sequence process counter-rotating resume module and be-encrypted data sequence are successively through the sequence after discrete Fourier transform (DFT) and the counter-rotating resume module; According to encryption parameter α and the real vector M V of dynamic encryption, the NV of Dynamic Selection, and by coefficient generation module generation weight coefficient w ₀, w ₁, w ₂, w ₃Be weighted summation to being weighted data sequence;

Three, the sequence of complex numbers after the weighting is carried out digital carrier modulation back output, be the signal after the encryption.

What 3, the four-item weight FRFT based on variable element according to claim 1 communicated by letter maintains secrecy and decryption method, it is characterized in that the concrete steps of deciphering are

(1), after the data that receive is changed through A/D, the coherent demodulation of at first carrying out digital carrier obtains in-phase component and quadrature component, and carrying out the Synchronous Processing of sequence after as the corresponding addition of imaginary part as real part, quadrature component with in-phase component, output sequence is sequence of complex numbers to be deciphered synchronously;

(2), to do parameter be the four-item weight class fractional Fourier transform of MV and NV for-α, the closely knit vector of dynamic resolution for the sequence of complex numbers for the treatment of deciphering, the sequence after the conversion is the sequence after the deciphering, can transfer to the base band demodulating module and carry out next step work.

4, according to maintaining secrecy and decryption method that claim 2 is communicated by letter with 3 described four-item weight FRFT based on variable element, it is characterized in that the dynamic change strategy of dynamic encryption parameter alpha is: the complete period B of dynamic encryption parameter alpha _α=4 have been divided into 8 groups, promptly are divided into α ₁, α ₂, α ₃, α ₄, α ₅, α ₆, α ₇And α ₈, each group is divided into 2 parts again, and wherein same group two parts at a distance of 2, correspond respectively to pseudo noise code and be 0 and the interval of 1 o'clock output parameter, B _FBe the size between each group parameter region, the parameter protection scope during each frame data conversion just, T _FBe the time that each frame data continues, T _CBe the cycle of parameter saltus step, T in the strategy _C=3T _F, this ratio can be adjusted as required, and the order of parameter transformation is in the strategy: α ₁, α ₆, α ₇, α ₃, α ₈, α ₂, α ₄, α ₅..., this is to set in advance in proper order.

What 5, the four-item weight FRFT based on variable element according to claim 4 communicated by letter maintains secrecy and decryption method, it is characterized in that the dynamic change strategy of real vector M V of dynamic encryption and NV is:

A, the variation strategy when each isolated component among real vector M V of dynamic encryption and the NV adopts same PN (pseudo noise code) sequence are:

A, when the period T of PN sequence in the parameter saltus step _CIn 4 frame period T are arranged _FThe time, the one-component m in the corresponding successively real vector of the frame of each PN sequence _iOr n _i(l=0,1,2,3), each component have only two kinds of value condition, and promptly 0 or 1;

B, when the period T of PN sequence in the parameter saltus step _CIn 16 frame period T are arranged _FThe time, the one-component in the corresponding real vector of per 4 PN sequence chips, promptly each component equals the decimal number that one 4 bit is represented;

C, when the period T of PN sequence in the parameter saltus step _C4 frame period T of interior less than _FThe time, with the period T of PN sequence in the parameter saltus step _CIn carry out periodic extension and make it have 4 frame period T _FAfter, implementation strategy a again;

D, when the period T of PN sequence in the parameter saltus step _C16 frame period T of interior less than _FThe time, with the period T of PN sequence in the parameter saltus step _CIn carry out periodic extension and make it have 4 frame period T _FAfter, implementation strategy b again;

B, the variation strategy when the real vector M V of dynamic encryption adopts different PN sequences with each isolated component among the NV or adopt the different original position of same PN sign indicating number are: each isolated component changes according to the rule of the PN sequence that is adopted.

What 6, the four-item weight FRFT based on variable element according to claim 5 communicated by letter maintains secrecy and decryption method, it is characterized in that it is by DSP, FPGA or FPGA+DSP realization.

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